The sine function can be evaluated via the following infinite series: sin(x) = x

Question

The sine function can be evaluated via the following infinite series: sin(x) = x x 3/3! + x 5/5! x 7/7! + · · · Write a function approxSine that takes as input two parameters, x and threshold, to perform the following task. Starting with the initial approximation sin(x) = x, add terms one at a time to improve this estimate until AbsoluteValue((true value approximation)/ true value) < threshold. Assume that the true value of sine is the one returned by the built-in sin function in MATLAB. Your function must return two output values: the approximate value of sin(x) and the number of terms that were needed to obtain this value subject to the desired error threshold.

Explanation / Answer

In on-line database theory, a useful dependency may be a constraint between 2 sets of attributes during a relation from a information. In different words, useful dependency may be a constraint that describes the link between attributes during a relation.

Given a relation R, a group of attributes X in R is claimed to functionally confirm another set of attributes Y, also in R, (written X Y) if, and on condition that, every X worth in R is related to exactly one Y worth in R; R is then aforementioned to satisfy the useful dependency X Y. Equivalently, the projection R} pi _}R may be a operate, i.e. Y may be a operate of X.[1][2] In straightforward words, if the values for the X attributes area unit acknowledged (say they're x), then the values for the Y attributes such as x is determined by wanting them up in any tuple of R containing x. typically X is termed the determinant set and Y the dependent set. A useful dependency FD: X Y is termed trivial if Y may be a set of X.

In different words, a dependency FD: X Y means the values of Y area unit determined by the values of X. 2 tuples sharing a similar values of X can essentially have a similar values of Y.

The determination of useful dependencies is a very important a part of coming up with databases within the relative model, and in information standardisation and denormalization. an easy application of useful dependencies is Heath’s theorem; it says that a relation R over associate degree attribute set U and satisfying a useful dependency X Y is safely split in 2 relations having the lossless-join decomposition property, particularly into (R)owtie pi _(R)=R} pi _}(R)owtie pi _{}(R)=R wherever Z = U XY area unit the remainder of the attributes. (Unions of attribute sets area unit typically denoted by mere juxtapositions in information theory.) a very important notion during this context may be a candidate key, outlined as a tokenish set of attributes that functionally confirm all of the attributes during a relation. The useful dependencies, in conjunction with the attribute domains, area unit elect thus on generate constraints that might exclude the maximum amount knowledge inappropriate to the user domain from the system as doable.

A notion of conditional relation is outlined for useful dependencies within the following way: a group of useful dependencies Sigma logically implies another set of dependencies Gamma , if any relation R satisfying all dependencies from Sigma additionally satisfies all dependencies from Gamma ; this can be sometimes written Sigma models Gamma . The notion of conditional relation for useful dependencies admits a sound and complete finite axiomatization, called Armstrong's axioms.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.